I've been using Flexicolor Final Rinse for both C-41 and B&W negatives for several months, and haven't seen any problems. As
@Anon Ymous pointed out, the C-41 Final Rinse contains stuff the B&W film doesn't need -- apparently because fungus likes dyes, but not so much silver (not sure why it doesn't attack the gelatin, which is nearly pure protein, however) -- but unless something in the fungicide attacks metallic silver, it shouldn't have any bad effects on B&W film.
The other advantage of the fungicide in C-41 Final Rinse is that the stuff won't mold the way PhotoFlo working solution will, so you can reuse it -- I'm still using the first two liters I mixed when I got my Cs41 kit back in May, and I've used up the capacity of that kit and I'm now about 18-20 rolls into Flexicolor replenished, plus a similar (if not greater) number of black and white rolls. No mold in the solution, and my negatives are still drying clean, so I'll let it run at least until it's time to mix fresh bleach and fixer for my Flexicolor.